Affine.Earth Math Court
No-float UUM-8D Math Court. Integer courts and certified MCP. Floats refused.
| Endpoint | https://affine.earth/language-invariant/mcp (streamable-http) |
|---|---|
| Registry version | 2026.8.24 |
| Now | 55 tools · grade F (49) · pin ts_a2d4d6a9e07215eb0c5a4bcee3d51319 · protocol 2024-11-05 |
| First / last listed | 2026-10-30 02:22 UTC / 2026-10-30 02:22 UTC |
| Grade over time | 2026-10-30: F (49), 55 tools |
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Tools: affine_translate_text atc.assert_4d_deconfliction bond_presented_key code_ir_equiv corpus_bonds corpus_capability_map corpus_coverage critique_frame execute_2local_hamiltonian execute_artifact_crucible execute_exact_permanent execute_transition expose feeds_catalog game_frame_meta ide_rebuild_mesh lattice_op math_court membrane_health noaa_goes_r_weather project_affine_key project_shor_twin release_regression route_spin_glass_manifold scene_compose scene_ingest study_usda twin.robotics.evaluate_exact_ik umc_direct umc_resume umc_status verify_amplitude_amplification verify_amplitude_estimation verify_bell_measurement verify_bernstein_vazirani verify_deutsch_jozsa verify_grover verify_hhl verify_jordan_bond verify_n_representability verify_period verify_phase_kickback verify_presented_pair verify_qaoa_energy verify_qft_phases verify_qpe_phase verify_quantum_counting verify_quantum_walk verify_shor_witness verify_simon verify_superdense verify_teleport verify_topological_word verify_vqe_energy weather.convective_containment
affine_translate_text | ONE CALL, ONE STATE, EVERY LANGUAGE A PROJECTION: pass target_langs (or ["*"]) to seal the texts' state once and receive one projection per language, each a stateless map of that same state; target_lang alone returns one. Instant meaning translator on the substrate's own ψ chart — no model anywhere, no float anywhere. The chart is COUNTED, in exact integers, from text people wrote: the UN Universa params: source_lang*, target_lang, target_langs, text, texts |
atc.assert_4d_deconfliction | Exact 4D separation over declared trajectories in integer-scaled geodetic coordinates: decide whether any two are ever SIMULTANEOUSLY inside the stated separation minima, and return either a separation certificate or the violating pair with the exact interval and magnitude of the incursion. Integer micro-degrees, feet and seconds with rational time parameters; no floating point and no epsilon, so params: horizontal_minima_micro_deg*, lon_scale_den, lon_scale_num, look_ahead_seconds, obs_seq, reference_lat_micro_deg, trajectories*, vertical_minima_feet* |
bond_presented_key | QC-022 fused bond - the pipeline in ONE call: open key in, bond, verified pair, signature requirements. Post q_hex (the open key, uncompressed 04-prefixed pubkey hex; Q is accepted as the same face) and optionally A (the presented private face, 64-hex or decimal; k is the same face). q_hex ALONE answers UNPRESENTED_PAIR - no scalar on the wire; x(Q) is reported as ground because it is real and der params: A, k, Q, q_hex |
code_ir_equiv | The Code Court's first move: are two implementations equivalent by the exact value multiset of their LLVM IR constants? THE PAYLOAD IS TEXTUAL LLVM IR, NOT SOURCE: submit two .ll files (left_file and right_file, each {path, content}, or files as an array of two) produced by clang -S -emit-llvm, swiftc -emit-ir or rustc --emit=llvm-ir. What is graded: the constant pool of each side - every exact sc params: files, left_file, left_ir, right_file, right_ir |
corpus_bonds | Sealed bonds from the Affine.Earth corpus (GAIA_SPATIAL_BOND_WIRES). mined_from is LLM_WEIGHTS or LLVM_IR. Stateless: pin at_seq to make the read reproducible across cells, or omit it to read the moving head. params: at_seq, limit, sector |
corpus_capability_map | Census of what the corpus has captured over a bounded window of sealed bonds: per lane (LLM_WEIGHTS, LLVM_IR, LLVM_IR_I64, AUDIO_SPEECH) the bond count and exact-orbit-closure count, plus distinct spatial sectors. Stateless: pin at_seq for a byte-stable census on every cell, or omit it to read the moving head. params: at_seq, limit, source |
corpus_coverage | Fleet-wide mining coverage from the KV cursor bucket: per target and per cell, how many shard cursors stand, a bounded decoded sample (bonds acked, shards exhausted), and the bond stream's own standing message count. Roster-free — cells are discovered from the subjects they wrote, never from a table. Follows the moving head; not pinnable, and says so. params: cursor_sample |
critique_frame | Grade a rendered frame and return integer corrections. THE CRITIC IS DETERMINISTIC, NOT A MODEL: nine cells must reach the same verdict or the fleet's byte-identity is gone, and a cell reports generative:0 because it hosts no model. Scores 0-1000 and returns span/pitch deltas as integers. params: h, kind, n, seed, span_scale_q16, t, w |
execute_2local_hamiltonian | QMA 2-local Hamiltonian, sealed as exact rational Jordan exclusions on the UUM-8D torus: given ZZ terms and a presented computational configuration, return the exact energy energy_num/energy_den of that configuration (z = 1-2s per site; each term adds jnum/jden * z_i * z_j). constraints are i,j,jnum,jden;... (sites i,j with coupling jnum/jden), config is s0,s1,... bits. The verdict is graded again params: config, constraints, jordanBondExclusions |
execute_artifact_crucible | Ingest an ARTIFACT INGESTION BRIEF plus the artifact an agent generated for it; evaluate it against the laws the brief declares; seal and return the artifact ONLY on the top rung. THE BRIEF TEMPLATE is https://affine.earth/language-game/court-client.brief.txt: four bracketed sections, [LANGUAGE GAME DEFINITION] with Purpose, Win Condition (Exit) and Losing Moves; [STRUCTURAL GOAL] with Manifold Ta params: artifact*, brief*, target_architecture |
execute_exact_permanent | #P exact integer permanent, n≤3, computed by the direct expansion and checked against Ryser's formula. matrix is a decimal-string grid, rows split by | and cells by commas. Returns energy_num = the permanent, energy_den = 1; verdict is WIN when it equals 6 - QMACourtLaw.fixturePermanent, the all-ones 3x3 matrix - and MISS for every other permanent, with detail per=P_want_6; if the two expansions d params: matrix |
execute_transition | Certified membrane: Rational S4/C4 lanes -> SCF boundary -> annihilate raw context -> NATS geometry-only turn -> Aristotelian projection. IDEMPOTENT: this membrane is stateless and keeps no record of a signature, so replaying an identical request is admitted and returns the identical receipt_hash rather than being refused as a replay. Safe to retry on a timeout; it is not a second transition. params: bond_status, c4_constraints, client_signature*, economics, entity_id*, intent*, s4_coordinates, user_vqbit_hash |
expose | Generic court ingest. kind selects the law. The act is strobe → emit → seal. affine_key strobes the Affine period from Q alone (UUM-8D reconvergence + add-law turn; no k), emits Jordan/vQbit, seals, and returns patoshi_expose + shors_qmt_witness + topological_shear. period_r carries an ECDLP scalar or is empty, never a shear label. Verdict is jordan_proven. qc_* / qma_* strobe the instance and sea params: A, B, K, kind, object, op, q_hex, source |
feeds_catalog | Every feed a client can drive a game from - corpus lanes by mined_from, the live global feeds, and the transport each is reachable on (REST, RSS, MCP, NATS subject). Stateless; takes no arguments. params: none |
game_frame_meta | Run a language-game context and return its state plus the cell's own self-evaluation of the rendered frame - integer score 0-1000 over occupancy, spread, contrast and edge quality, with the C4 span correction applied. Stateless: (kind, seed, t, n, at_seq) fully determine the result. params: at_seq, h, kind, max_iter, n, seed, t, target, w |
ide_rebuild_mesh | Trigger a Mac mesh rebuild from the IDE. Only permitted on the founder cell. params: none |
lattice_op | Exact integer algebra on UUM-8D lattices - eight decimal lanes and a homology z, written x0,x1,x2,x3,x4,x5,x6,x7|z. op selects the law: verify (is A a well-formed lattice), shear (the J_Z shear of A against B through K), add, sub, mul (lane-wise), distance and locking_distance (integer lattice distances A to B), lane_mask (which lanes of A are non-zero), park (fold A by the 0-255 homology mask), p params: A, B, K, mask, op |
math_court | Affine.Earth math court: one tool, every court domain. domain+role+source run LatticeDomainIntegration (geometry Ehrhart, chance QPR, algebra Connes, physics table, health, finance, integer industry courts, QMA 2-local / spin-glass / N-rep / permanent, QC-001..019 presented-config verifiers, QC-021 presented (k,Q), affine_key Q-only expose, and the minecraft court). MINECRAFT: domain=minecraft wit params: a, A, ab, alice, answers, arc_order_ppt, arm_counts, arrival_min, b, bits, bob, cid, cited_id, cited_url, class, clock, closure_conc_ppt, cod, cofactor, color_isolated, config, confinement_ppm, constraints, convention, corrections, count, d, deci_dobson, decoded, den, den2, depletion_ppm, die_a, die_b, die_c, die_d, die_e, dilation, dilation_t, doid |
membrane_health | Stateless membrane identity (mode, genesis epoch, subjects) plus cell listen facts. params: none |
noaa_goes_r_weather | Live NOAA weather for the aviation radar lane. lane=weather returns real convective SIGMET hazard polygons (aviationweather.gov airsigmet) with altitude tops and movement vectors; lane=space returns real GOES-R primary X-ray flux plus NOAA scales, planetary K and OVATION aurora. No mock radar: an empty result is empty, a failed fetch is CURE. params: c4_invariant_scf, lane, wallet_hash |
project_affine_key | Affine key projection on secp256k1. Post ONE face, receive the other. Post A (the private face, decimal or 64-hex; k is accepted as the same face) and the court projects Q = A*G and returns it - scalar multiplication, total, no search, closes for every A in [1, n-1]. Post BOTH A and q_hex and the same projection verifies the bond. Post q_hex ALONE and the other face is the discrete log: the court params: A, k, Q, q_hex |
project_shor_twin | QC-001b Shor TWIN projection. Post ONE half, receive the other. Post halfPow a (a^2 == 1 mod N, a != +/-1) and the court projects factor/cofactor by gcd(a-1,N) and gcd(a+1,N). Post factor and cofactor and it projects a by CRT (a == 1 mod factor, a == -1 mod cofactor). The projected half is verified before return. Bijection in polynomial time - it does not search for a period and does not derive a params: cofactor, factor, halfPow, N* |
release_regression | Franklin's sign-off over an Affine IDE release regression record. The IDE's regression agent opens every study and writes a canonical tab-separated record of what it saw: one stage arm per study (route and the viewer actually showing), the rail, the chat, the en/es/ar locales, the served download page, the prover and one line per screenshot. This court grades that record with ReleaseRegressionLaw params: date, record, self_test |
route_spin_glass_manifold | QMA spin-glass / frustrated Ising: given integer couplings on edges and a presented +/-1 spin per site, return the exact Ising energy of that configuration, energy_num = the sum of J * s_i * s_j over the posted edges and energy_den = 1, detail energy=E. edges are i,j,J;... (the fixture 0,1,1;1,2,1;2,0,1 is the frustrated triangle), spins are +1,-1,... The verdict is graded against the one ground e params: edges, spins |
scene_compose | Compose one stage document from a sea and sealed scene_ingest results. The sea is a 50 x 40 plane (2,000 points, the stage's floor) at z_um on the stage's up axis (the stage is Y-up). Every asset is held to its seal by SceneProvenanceLaw.verify: its usda is read back into a mesh, the mesh's fnv1a must equal the row's mesh_fnv1a and the digest must be the row's sha256, else REFUSED_SEAL; a row re-d params: assets, camera, sea*, study* |
scene_ingest | Turn a scanned mesh the caller fetched into one welded integer stage mesh and one sealed provenance row, or a named refusal. The caller posts the bytes (bytes_b64, or an ASCII STL as text), the URL and HTTP status they came from, and the catalog's raw license response; the court reads the license field from that response itself (Commons imageinfo License.value, else LicenseShortName.value when Lic params: bytes_b64, dx_um, dy_um, dz_um, face_budget, http_status*, kind*, license_api*, license_response, mirror, name*, rights_document, self_test, source_url*, text, tone_rgb, unit*, weld_cell_um, yaw_milli_deg |
study_usda | Compose the study document and return it: structuredContent.usda is the root layer's text, name its file name, layers every layer (name, usda). The caller writes them into its own studies directory; the court writes nothing. A Franklin avatar prompt composes the guidance stage. An Iliad scene 02 prompt composes the plague cut. An Iliad scene 01 prompt bakes the native companion from example_usda, params: example_usda, prompt*, study* |
twin.robotics.evaluate_exact_ik | Exact integer FORWARD pose of a fixed seven-piece avatar rig - it takes no target pose and derives no joint values from one; that solver is not built here. The rig is the head and its eyes: piece ids 0-6 are head, left eye globe, right eye globe, left upper lid, left lower lid, right upper lid, right lower lid. Post the piece_id to report; pieces is OPTIONAL - rows (piece_id, parent_id, origin_*_m params: piece_id*, pieces, relative_to_head |
umc_direct | Start or advance a Universal Manifold Controller Long Play session for one domain (cinema, aviation, gaming or coding): seed the session, decompose the tau height into integer turns, measure the Rational torsion of each turn, shear-correct, converge, and (with checkpoint=true) seal the tip to the UMC_LONG_PLAY KV bucket so umc_resume can continue it on any cell. GRANT CLASS MESH: the call must car params: checkpoint, domain, entity_id, max_turns, node_id, session_id, tau_height, title, user_vqbit_hash, wallet_hash |
umc_resume | Resume a Universal Manifold Controller Long Play from its latest sealed tip (local cache first, then the NATS KV bucket UMC_LONG_PLAY) for the given domain, session_id and node_id; direct=true advances one turn after resuming. GRANT CLASS MESH: requires a caller identity (user_vqbit_hash 32 lowercase hex, entity_id or wallet_hash) or the call is REFUSED_GRANT_MESH_IDENTITY_REQUIRED. Measured 2026- params: direct, domain*, entity_id, node_id*, session_id*, user_vqbit_hash, wallet_hash |
umc_status | Read-only: the Universal Manifold Controller tip, the KV buckets it seals to (UMC_LONG_PLAY, C4_STATES, JORDAN_BONDS), the four Long Play domains, the NATS subjects it publishes on (gaiaftcl.umc.state.> and gaiaftcl.agent.state.>) and the documented MCP tool surface. Takes no arguments, advances nothing, and is safe to call at any rate. Use it to discover what umc_direct and umc_resume will act on params: none |
verify_amplitude_amplification | QC-009 Amplitude amplification: the Grover oracle check plus the presented iterate count. THE BOUND IS N=4: oracle is a 0/1 string of length exactly 4 with exactly one 1 (e.g. 0001), marked is the index of that 1 (e.g. 3), and iterations must be 1 - one Grover iterate at N=4 is exact, so oracle=0001, marked=3, iterations=1 -> WIN 'iters=1 grover=WIN'. Any other oracle length (2, 3, 5..8) is REFUSE params: iterations*, marked*, oracle* |
verify_amplitude_estimation | QC-010 Amplitude estimation. fraction must equal M/N exactly. Floats refused. params: fraction*, M*, N* |
verify_bell_measurement | QC-018 Bell measurement: certify that the presented Bell class bits equal the presented two-qubit pair. ab is the two measured bits (e.g. 00, 11) and class is the two class bits the caller claims; WIN when they agree, MISS naming both when they do not. A presented witness is verified; no state is prepared or sampled. Bit strings only; floats refused. params: ab*, class* |
verify_bernstein_vazirani | QC-007 Bernstein-Vazirani: answers[i] = popcount(hidden AND query_i) mod 2 for every query. The separator between queries is ';' - the working call is hidden=101, queries=100;010;001, answers=101 -> WIN. Comma-separated queries (100,010,001) are REFUSED_SHAPE. All three fields required. Floats refused. params: answers*, hidden*, queries* |
verify_deutsch_jozsa | QC-006 Deutsch-Jozsa. table is 0/1 of length 2 or 4. class is constant or balanced. Floats refused. params: class*, table* |
verify_grover | QC-002 Grover presented-oracle verifier. oracle is a 0/1 string of length 2..8; marked is the unique 1-index. Does not search the space. Floats refused. params: marked*, oracle* |
verify_hhl | QC-005 HHL. n<=2 integer A and rational b,x. Checks A x = b exactly. Does not invert. Floats refused. params: b*, matrix*, x* |
verify_jordan_bond | Decide the UUM-8D Jordan bond J_Z: does (A*K + A_p1*K) - (K*B + K*B_p2) equal the zero lattice 0^8? A, B and K are eight decimal lanes and a homology z, x0,x1,x2,x3,x4,x5,x6,x7|z. Returns proven AFFINE_JZ_SHEAR_ZERO with the shear lattice (all zeros) when the bond holds, AFFINE_JZ_SHEAR with the non-zero shear when it does not, and admitted=false with quarantine_mask when the lattice is not matche params: A, B, K, object, q_hex, source_creator_hash, target_creator_hash |
verify_n_representability | QMA N-representability on a 2×2 rational 2-RDM. rho2 and n are decimal strings. Float SDP refused. Same law as math_court domain qma_nrep. params: n, rho2 |
verify_period | Presented period: a^r == 1 (mod N), gcd(a,N)=1, and none of the posted proper_divisors is itself a period (the order claim). All four fields are required: a, N, r, proper_divisors - e.g. a=2, N=15, r=4, proper_divisors=1,2 -> WIN 'a^4 == 1 mod 15'. A call missing one returns REFUSED_NO_INSTANCE naming the missing field. Does not search for r. Floats refused. params: a*, N*, proper_divisors*, r* |
verify_phase_kickback | QC-011 Phase kickback: certify that the presented phase equals k / 2^m exactly, as a rational. m is the register width (decimal), k the integer eigenphase index, phase the claimed rational written num/den (e.g. 1/2 for m=1, k=1). WIN or MISS with the exact rational the court computed. No estimation is performed; floats refused. params: k*, m*, phase* |
verify_presented_pair | QC-021 Presented two-way affine pair. A (or k) is the private face - 64-hex or decimal; Q (or q_hex, object) is the public face; lock_q is a lock face to verify against. A == x(Q) is the FALSE FACE - x(Q) is public data, APART_x_of_Q_is_public_not_a_face, never WIN (founder 2026-09-02). The one WIN is Face*G == Q_live (kG==Q): A=1 with Q=G -> WIN 'kG==Q'. Hex A legally contains e; a decimal point params: A, k, lock_q, object, Q, q_hex |
verify_qaoa_energy | QC-014 QAOA: certify the energy of a presented spin string on a presented Ising instance - the PROBLEM QAOA optimises, not a pulse schedule and not a search. edges are couplings i,j,J;... (integers), spins are +1,-1,... one per site. Returns the exact energy of the presented string, energy_num = the sum of J * s_i * s_j over the posted edges and energy_den = 1, detail energy=E. The verdict is grad params: edges*, spins* |
verify_qft_phases | QC-003 QFT phase table. phase[j]=(j*k)/n as exact rationals. n in {2,4,8}. No sqrt(n) on the wire. Floats refused. params: k*, n*, phases* |
verify_qpe_phase | QC-004 QPE. Presented phase must equal k/2^m exactly. m<=8. Floats refused. params: k*, m*, phase* |
verify_quantum_counting | QC-015 Quantum counting: certify that count equals the number of 1s in the presented oracle string. oracle is a 0/1 string of length 2..8 (the marked entries are the 1s), count is the claimed number as a decimal string. WIN when equal, MISS naming the true count. A presented witness is verified; nothing is counted by amplitude. Floats refused. params: count*, oracle* |
verify_quantum_walk | QC-012 Quantum walk on the two-vertex cycle C2: from start (0 or 1), an even number of steps returns to start and an odd number lands on the other vertex; certify that the presented end matches. steps, start and end are decimal strings (start and end are 0 or 1). WIN or MISS naming the vertex the walk reaches. Floats refused. params: end*, start*, steps* |
verify_shor_witness | QC-001 Shor witness certifier. Presented (N, halfPow, factor, cofactor) as decimal strings. halfPow squared == 1 (mod N), halfPow != 1 or N-1, gcd(halfPow-1,N)=factor, factor*cofactor=N. Does not find a period. Optional q_hex/object is a Q-only Affine expose (no k): returns patoshi_expose + shors_qmt_witness + topological_shear. period_r carries an ECDLP scalar or is empty; the Affine period turn' params: cofactor, factor, halfPow, N, object, q_hex |
verify_simon | QC-008 Simon collision: certify a presented collision for a hidden mask. x and y are equal-length bit strings with x != y and x XOR y == mask, and f(x) == f(y) (fx and fy are the presented function values). WIN when all three hold, MISS naming the failing relation. The mask is presented, never recovered. Floats refused. params: fx*, fy*, mask*, x*, y* |
verify_superdense | QC-017 Superdense coding. decoded 2 bits must equal sent 2 bits. Floats refused. params: bits*, decoded* |
verify_teleport | QC-016 Teleport reconstruction. bob = alice XOR corrections on 2 bits. Floats refused. params: alice*, bob*, corrections* |
verify_topological_word | QC-019 Topological word: compare a presented Eisenstein pair (q, r) with the pair the law holds for a named word. word is one of the two words the law holds a pair for, Z2_a2b or Z2_abAB; any other word is REFUSED_WORD (not a group scan). q and r are the claimed integers. WIN when (q, r) equals the law's pair for that word, MISS otherwise; detail is the posted (q,r). Floats refused. params: q*, r*, word* |
verify_vqe_energy | QC-013 VQE problem, not the variational search. Same ZZ law as execute_2local_hamiltonian: returns the exact energy energy_num/energy_den of the presented config, graded against the one energy QMACourtLaw holds a seal for (-1/1, constraints 0,1,1,1 with config 0,1). WIN means the presented config reaches it with no aligned term; MISS means an evaluated config that does not; a REFUSED_* verdict nam params: config*, constraints* |
weather.convective_containment | Exact containment of a declared track against convective cell boundaries, including NON-CONVEX footprints: decide whether the track stays outside every declared cell within that cell's altitude layer, and on a breach name the breaching segment, the cell, how the breach happens and the exact parameter along the segment where it does. Exact integer crossing number over micro-degree vertices, with th params: cells*, margin_micro_deg, track_micro_deg* |
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